Penrose limits of homogeneous spaces
arXiv:math/0405506 · doi:10.1016/j.geomphys.2005.08.002
Abstract
We prove that the Penrose limit of a spacetime along a homogeneous geodesic is a homogeneous plane wave spacetime and that the Penrose limit of a reductive homogeneous spacetime along a homogeneous geodesic is a Cahen--Wallach space. We then consider several homogenous examples to show that these results are indeed sharp and conclude with a remark about the existence of null homogeneous geodesics.
16 pages, many changes particularly to sections 6 and 7
References in corpus (14)
- Strings in flat space and pp waves from Super Yang Mills
- Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background
- Penrose limits and maximal supersymmetry
- Exactly solvable model of superstring in Ramond-Ramond plane wave background
- Penrose limits, supergravity and brane dynamics
- Plane Wave Limits and T-Duality
- Homogeneous fluxes, branes and a maximally supersymmetric solution of M-theory
- Homogeneous Plane Waves
- Solvable model of strings in a time-dependent plane-wave background
- Solvable models of strings in homogeneous plane wave backgrounds
- Penrose Limits and Spacetime Singularities
- Homogeneity and plane-wave limits
- Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves
- Kaigorodov spaces and their Penrose limits
Cited by in corpus (10)
- Homogeneous geodesics in homogeneous Finsler spaces
- Locally homogeneous pp-waves
- Exact Parallel Waves in General Relativity
- Symmetric M-Theory Backgrounds
- Homogeneous geodesics of left invariant Finsler metrics
- The existence of light-like homogeneous geodesics in homogeneous Lorentzian manifolds
- Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three
- Homogeneous Geodesics in Generalized Wallach Spaces
- On the Geometric Orbit Property for Lorentz Manifolds
- Pseudo-Riemannian Weakly Symmetric Manifolds